\section{Conclusions and Future Work}

We presented a novel approach for skilled collaborative team formation based on finding dense subgraphs. On the theoretical front, we showed a $3$-approximate algorithm. On the practical side, we showed several heuristic improvements to this algorithm and compared it to a previous approach based on identifying small diameter subgraphs. Our experimental results show that the densest subgraph approach significantly outperforms the previous work on multiple different measures of collaborative compatibility. 

%Several questions remain open. 
The formulations in this paper as well as~\cite{LLT} assume that for any given skill, each node in the network is either skilled or not skilled. A nice generalization would be to consider a range of expertise for any skill, modeled as a value between $0$ and $1$.
%, rather than binary.
Another specific open question is to present more efficient 
%(specifically linear-time) 
algorithms for all objectives. 
%main algorithm that we presented as well as the provable algorithms from Lappas et al.~\cite{LLT} are quite inefficient, and obtaining 
%in the worst case, have a time complexity cubic in the number of nodes. A question is to find 
%better linear time algorithms would be interesting. 
%without sacrificing the connectivity of the resulting solution. 
%Another direction for future work is to see how different techniques perform when the number of skills involved in the graph is larger. 
%
Further, these definitions can be extended along many dimensions. 
%Skills are never binary (i.e. expertise of different people for a specific skill 
%For example, while nodes are selected into a team based on multiple skills they possess, 
In reality a team's 
%skills and collaboration prospective depending 
value depends
on several complex assets such as
% time constraints, 
%a node's contributions eventually are limited also by time constraints. Further, there are other assets of nodes that may contribute to a team's compatibility, such as their affiliation institutes, 
cultural backgrounds, geographical location, personalities, ability to work in teams etc. 
Some of these characteristics cannot even be measured easily. 
%, and thereby make the team formation problem very complex in reality. The current formulations do not address these issues. 
%While the 
Yet, while the current models are a good start, it would be nice to investigate these directions and move closer to the motivating realistic scenario.

%However, team formation definitions can be extended along many dimensions. 
%%Skills are never binary (i.e. expertise of different people for a specific skill 
%%For example, while nodes are selected into a team based on multiple skills they possess, 
%In reality a team's 
%%skills and collaboration prospective depending 
%value depends
%on several more complex assets such as time constraints, 
%%a node's contributions eventually are limited also by time constraints. Further, there are other assets of nodes that may contribute to a team's compatibility, such as their affiliation institutes, 
%cultural backgrounds, geographical location, personalities, skill expertise measured as a range, ability to work in teams etc. 
%%Some of these characteristics cannot even be measured easily.
%%, and thereby make the team formation problem very complex in reality. The current formulations do not address these issues. 
%Further, for both, the main algorithm that we presented as well as the provable algorithms from Lappas et al.~\cite{LLT},
%%in the worst case, have a time complexity cubic in the number of nodes. A question is to find 
%it would be interesting to find better linear time algorithms.
%%without sacrificing the connectivity of the resulting solution. 
%%Another direction for future work is to see how different techniques perform when the number of skills involved in the graph is larger. 
%%
%While the current models are a good start, these additional measures and time-complexities leave several questions open for further study in order to move closer to the motivating realistic scenario.

%\noindent {\bf Acknowledgements.} We thank Barna Saha for helpful comments.